# Performance Analysis of a H-Darrieus Wind Turbine for a Series of 4-Digit NACA Airfoils

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## Abstract

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## 1. Introduction

## 2. Rotor Aerodynamic Performance

_{N, T}are the aerodynamic blade load components, normal and tangential, respectively; V

_{0}is the wind velocity; ρ is the air density; A is the reference surface; in this work, A = c∙1, where c is the length of the chord, and 1 is the unit span of the blade. The tip speed ratio is defined as the ratio of tangential blade velocity V

_{T}and wind velocity:

_{x}, and a perpendicular component, V

_{y}. These velocities were calculated using a rake that consists of 100 checkpoints, positioned at a distance of 1.5 R downstream behind the rotor axis of rotation, as shown in Figure 4. The total length of the rake was 3∙R, similar to the case of the experiments of Tescione et al. [54,55]. The velocity components V

_{x}and V

_{y}vary in time, but this paper presents their average values according to the formula:

## 3. Numerical Model

#### 3.1. Geometric Modeling

#### 3.2. Numerical Settings

#### 3.3. Computational Mesh

^{6}m, which provides an average wall y+ of 0.50 for TSR = 2 and of 0.53 for TSR = 6. The growth rate of unstructured mesh elements is 1.04. The final grid shown in Figure 5 consists of 234,840 elements and 136,059 nodes. The computational grid with global settings described above was used also by Rogowski [19]. This author showed that these mesh settings provided sufficiently accurate results of the velocity fields and aerodynamic blade loads.

#### 3.4. Mesh Sensitivity Study

_{P}, is for N / 4, i.e., for a number of divisions equal to 50. An increase in the number of elements above 200 does not cause a significant change in C

_{P}but leads to an increase in computational costs, Figure 6.

#### 3.5. Initial Condition Effects

_{S}is the projected area seen by the wind, defined as = 2R∙1, where 1 is a unit span of the blade. The maximum values of the torque coefficient reach an almost constant values in each rotor revolution of about 1.3 after approximately 12 complete rotor revolutions. After 19 full turns, the differences are at the level of the second decimal place. The minimum values of this torque coefficient are about 0.03 after 12 full rotations of the rotor. A similar conclusion was made by Rogowski [19], who studied the effect of initial conditions by simulating 50 full rotor revolutions. Here, the simulation showed that 15 full revolutions of the rotor was sufficient to obtain repeatable results of both aerodynamic blade loads and velocity profiles behind the rotor.

## 4. Model Validation

#### 4.1. RANS Approach Validation Based on Measured Static Data for NACA 0018

^{9}method to find the location of the transition point. Inviscid formulation, governing equations for viscous formulation, and compressibility correction implemented in the interactive XFOIL are presented, among others, by Mark Drela [65].

_{0}for steady-state simulations. The undisturbed flow velocity in RANS simulations is equal to the tangential velocity of the rotating rotor blade, V

_{0}= ωR. In these investigations, it was assumed that the angular velocity of the rotor was constant for all tip speed ratios and equal to 8.18 rad/s. Knowing that the rotor radius is 8.48 m, the tangential velocity of the rotor blade is 69.4 m/s for the Reynolds number to be equal to 2.9 million. Aerodynamic force coefficients, lift coefficient C

_{L}, and drag coefficient C

_{D}are defined as:

_{L}curve is practically a straight line up to the angle of attack of 12–13 degrees. The aerodynamic derivative (dC

_{L}/dα) of the experimental C

_{L}curve for the angle range of 0–12 degrees is 5.681 per rad. The aerodynamic derivative of the C

_{L}curve from CFD is larger by 3.4% compared to the experiment, whereas the aerodynamic derivative from XFOIL is larger by 11% compared to the experiment. The minimum drag coefficient corresponds to the zero angle of attack and is 0.0076 for the experiment, 0.0061 for XFOIL, and 0.01 for CFD. The somewhat larger minimum drag for the CFD is most likely because transition was not considered.

_{D}and C

_{L}coefficients. The next important reason is the low-Re flow regime that results in various transient phenomena on the airfoil surface. Unlike the method implemented in the XFOIL code, the k-ω SST turbulence model used in presented CFD simulations does not include any transition phenomena in its formulation.

_{crit}. Above this critical angle of attack, the differences in lift characteristics are visible. Analyzing the aerodynamic derivative dC

_{L}/dα in the range of the angle of attack from α

_{crit}to 18 degrees (the maximum angle of attack analyzed using the RANS approach), it was found that, for the NACA 0012 airfoil, it is −0.11, and, for the NACA 0015 airfoil it is equal to −0.03, while, for the NACA 0018 airfoil, it is −0.005 [64]. In the case of CFD analysis, these derivatives are, respectively, 0.17, 0.033, and 0.0051. This analysis shows that, for the NACA 0018 and NACA 0015 airfoils, the decrease in lift force is milder compared to the NACA 0012 airfoil. Figure 9 shows that the lift coefficient characteristics for NACA 0015 and NACA 0018 do not experience a sudden drop after the static stall angle. The mild stall for NACA 0018 and NACA0015 airfoils at the given Reynolds number it comes from a gradual upstream movement of the trailing edge separation. In the case of symmetric airfoils, such as NACA 0012, a sharp stall is observed [66]. As can be seen from Figure 9, the results of the lift coefficient for the NACA 0012 airfoil are slightly worse compared to the experimental results by Sheldahl and Klimas [64].

#### 4.2. Instantaneous Aerodynamic Blade Loads

## 5. Results and Discussion

#### 5.1. Aerodynamic Loads on a Rotor Blade for Symmetrical 4-Digit NACA Airfoils

^{6}, it can be stated that the airfoil with a relative thickness of 12% achieves the highest value of the maximum lifting force coefficient; however, the critical angle of attack is smaller compared to the NACA 0018 airfoil. If the blade pitch angle is zero, the geometric angle of attack is measured between the relative velocity and the wind velocity. At the tip speed ratio of 2, the azimuthal angle of 52 degrees corresponds to the local geometric angle of attack of 16.7 degrees. The effective angle of attack is of course lower than the geometric angle of attack because the flow velocity at the rotor is lower than the wind speed. However, this difference is not very large, especially in the upwind part of the rotor [1]. Therefore, for the NACA 0012 airfoil and at the azimuth of 52 degrees, flow detachment and consequent loss of lift may be expected. In addition, in the case of the NACA 0012 airfoil, the decrease in lift above the critical angle is much more rapid, indicating a leading edge stall, than in the case of NACA 0015 and NACA 0018 airfoils, for which the decrease in lift is much milder and where the separation starts at the trailing edge and gradually increasing with the angle of attack. It can also be seen from Figure 11 that the tangential blade load coefficient decreases rapidly in the downwind part of the rotor at azimuth around 200–235 degrees deepening on the relative thickness of the airfoil. In the case of low tip speed ratios, local angle of attack on both rotor sides exceeds critical values. Therefore, local decreases in tangential force observed in this part of the rotor result from exceeding the critical angle of attack. The differences between aerodynamic blade load coefficients for higher tip speed ratio of 5 are practically invisible to the naked eye. In general, all analyzed airfoils give an almost identical distribution of aerodynamic blade loads. However, a subtle difference can be seen for an azimuth of about 95 degrees, where the peak of the tangential blade load first increases with the thickness of the airfoil and then decreases. Song et al. [31], who also analyzed the aerodynamic performance of a Darrieus rotor with higher solidity and with symmetrical NACA 00XX airfoils, obtained a similar correlation. In the optimum tip speed ratio range, the maximum power coefficient was achieved by the rotor with NACA 0015 airfoils.

_{x}and v

_{y}are flow velocity components. For better readability, the vorticity results were limited to a range from −1000 1/s to 1000 1/s. Red represents the anti-clockwise direction, and blue represents the clockwise direction. This figure clearly shows that, in the case of the NACA 0012 profile for θ = 54–60 degrees, a large anti-clockwise vortex appears on the leading edge. The same phenomenon also appears for the NACA 0015 airfoil, however, only on a smaller scale and for larger azimuths than in the case of the NACA 0012 airfoil.

_{P}around 0.5) for the NACA 0015 airfoil shifts towards higher tip speed ratios. Moreover, the thicker airfoil (NACA 0018) is slightly worse at a tip speed ratio of 6 than the NACA 0015 airfoil.

#### 5.2. Aerodynamic Blade Loads for Cambered 4-Digit NACA Airfoils

_{T}curves have the same value close to zero for an azimuth close to 180 degrees. This is the location where the chords of the airfoils are parallel to the wind direction and the wind blows from the back. All curves also have a very similar value of about −0.38 when the blade passes through an azimuth of 13 degrees. The ratio of the maximum values of the tangential blade load for the upwind part of the rotor to the maximum values of this load for the downwind part as a function of maximum airfoil camber can also be approximated by a straight line. This ratio reaches a value from 11.6 for the NACA 0018 airfoil to 1.34 for the NACA 4418 airfoil. Thus, for the airfoil with the largest maximum camber examined, the tangential blade load peak on both sides of the rotor area is almost equal. The decrease in the tangential blade load for the NACA 0018 airfoil (Figure 14) can also be caused by so-called virtual blade camber. It is caused by a curved flow field caused by the revolution of the wind turbine rotor. Airfoil characteristics are usually measured in a wind tunnel with straight flow field. The curved flow field causes the symmetrical airfoil of a vertical axis wind turbine to work as a cambered airfoil. This causes a change in the lift coefficient characteristics of the airfoil. For a given angle of attack, the value of the lift coefficient of the symmetrical airfoil with the “virtual camber” is lower compared to the symmetrical airfoil in straight flow field [71].

_{N}distributions for the different airfoils investigated are very similar, whereas, for a tip speed ratio of 5, the curves are very similar, but they are offset by almost constant value from one another. A detailed analysis of the normal component of the aerodynamic blade load for a tip speed ratio of 2 shows, however, that, as in the case of TSR = 5, the behavior of the curves is identical, the curve offset is also visible, although the value of the offset of the curves is very small. Only the curve corresponding to the NACA 0012 airfoil has a different shape from the others and as already described, it is associated with a sudden loss of lift on this profile. It can be seen that, in the 0–60-degree, 164–226-degree, and 314–360-degree azimuth ranges, the trends of both CF

_{T}and CF

_{N}for TSR = 2 are identical to those for TSR = 5. In the upwind part of the rotor, the absolute value of the maximum normal blade load coefficient decreases almost linearly with the maximum camber of the airfoil from 29.2 for the NACA 0018 airfoil to 17.7 for the NACA 4418 airfoil, whereas the CF

_{Nmax}in the downwind part of the rotor increases almost linearly from 7.63 for the NACA 0018 airfoil to 20.13 for the NACA 4418 airfoil. The slopes of straight lines passing through CF

_{Nmax}as a function of maximum airfoil camber are −2.865 for the upwind part of the rotor and 2.993 for the downwind part of the rotor. In the case of TSR = 2, the slopes are also very similar, at −0.591 for the upwind part of the rotor and 0.63 for the downwind part of the rotor; however, in the case of TSR = 2, the NACA 0018 profile was not used for the analysis. For TSR = 5, the ratio of maximum normal blade load coefficient in the upwind part of the rotor to the downwind part of the rotor is from 3.82 for the NACA 0018 airfoil to 0.88 for the NACA 4418 airfoil, while, for TSR = 2, this ratio is from 1.72 for the NACA 1418 airfoil to 1.2 for the NACA 4418 airfoil.

#### 5.3. Aerodynamic Wake for Symmetrical and Cambered 4-Digit NACA Airfoils

_{x}and V

_{y}, downstream behind the rotor. Both velocity components are related to the wind velocity V

_{0}, while the coordinate y (please see Figure 4) is normalized by the radius of the rotor R. The velocity results presented in Figure 18 are given for the NACA 0018 airfoil. It is easy to see that the rotor has a greater effect on the velocity component V

_{x}than on the component perpendicular to the wind direction V

_{y}. As tip speed ratio increases, the velocity V

_{x}decrease is larger. The average velocity of each of these profiles decreases almost linearly as a function of tip speed ratio from 0.92 for TSR = 2 to 0.57 for TSR = 6. It also seems that, except in the case of TSR = 2, the velocity component V

_{x}profiles are almost symmetrical. In the case of velocity component V

_{y}, its average for each tip speed ratio value is very close to zero. When analyzing the distribution of this velocity component, the more important factor visible to the naked eye is the slope of the function V

_{y}/ V

_{0}(y / R). In this discussion, we have limited our considerations for the y / R ratio range from -1 to 1 because in this range the

_{Vy/V0}curves are the most linear. For tip speed ratio 2, the curve slope $d\left({V}_{y}/{V}_{0}\right)/d\left(y/R\right)$ is small and is 0.014, whereas, for tip speed ratio 5, the slope is 0.0515. It is easy to see from Figure 16 that the change in the slope of these curves with tip speed ratio is not linear. In order to better illustrate this, a graph of the slope as a function of tip speed ratio was prepared (see Figure 19). From this figure, it can be seen that, as the tip speed ratio increases, the increase in slope is getting smaller.

_{y}is very small compared to the component V

_{x}. The average value of velocity component V

_{y}/ V

_{0}of all velocity profiles is 0.0028 and is smaller by about 99.6% compared to the average V

_{x}/ V

_{0}of all velocity profiles. To better show the share of both components of velocity ratios, a vector graph of velocity ratio V/V

_{0}was made for two tip speed ratios values, 2 and 6 (Figure 20). The speed V is defined as the root of the sum of the squares of the components V

_{x}and V

_{y}. The figure clearly shows that the velocity vectors for TSR = 6 are more deflected outwards at the coordinate | y / R | = 1.5 than in the case of TSR = 2.

_{x}and V

_{y}in the aerodynamic wake downstream behind the rotor for two tip speed ratios 3 and 6 depending on the relative thickness of the airfoil. Velocity distributions are given for four symmetrical airfoils: NACA 0012, NACA 0015, NACA 0018, and NACA 0021. This figure clearly shows that, except for the NACA0012 airfoil at the tip speed ratio of 3, the differences in the velocity profiles downstream behind the rotor, both the V

_{x}and V

_{y}components, are negligible. The average value of all velocity profiles V

_{x}/V

_{0}for TSR = 3 is 0.81 with a standard deviation of 0.014, whereas, in the case of the velocity profiles V

_{y}/V

_{0}, the average value is −0.0049, with a standard deviation of 0.0023. For a tip speed ratio of 6, the average velocity of all V

_{x}/ V

_{0}velocity profiles is 0.01173 with a standard deviation of 0.0117. The average value of the second velocity component for all V

_{y}/ V

_{0}velocity profiles is 0.0004, with a standard deviation of 0.001. Based on the average velocity values and the standard deviation, it can be stated that the share of the velocity component parallel to the wind direction is larger than in the case of the velocity component V

_{y}and that the differences in the velocity profiles downstream behind the rotor are lower in the case of the velocity component V

_{y}.

_{x}/ V

_{0}curves seem to be very close to each other, while the V

_{y}/ V

_{0}curves seem to be offset by some fixed value. Analyzing the average values and standard deviations, it can be seen that both in the case of the velocity component V

_{x}and V

_{y}, the differences between the results are very small, both for in the case of TSR = 3 and TSR = 6. For TSR = 3, the average velocity of all three V

_{x}/ V

_{0}velocity profiles is 0.57 and the standard deviation is 0.007; the average velocity for all V

_{y}velocity profiles is −0.007 with a standard deviation of 0.0068. In the case of TSR = 6, the average velocity of the three average V

_{y}/ V

_{0}velocity profiles is 0.797 with the standard deviation equal to 0.0054, whereas, in the case of the second velocity component, the average velocity is −0.012, with standard deviation of 0.0052. The slopes of the V

_{y}/ V

_{0}curves in the range of y / R from −1 to 1 are almost identical and are on average 0.037 for TSR = 3 and 0.05 for TSR = 6.

## 6. Conclusions

- Steady-state simulations confirmed that the numerical model and computational mesh give reasonable results of aerodynamic force coefficients, lift, and drag components. ANSYS Fluent, Release 17.1 better predicts the relationship between lift and angle of attack, while XFoil gives a slightly better result of a minimum drag coefficient compared to the experiment. Other numerical codes, like FLOWer CFD and vortex model, have shown that ANSYS Fluent CFD code correctly estimates the unsteady blade load components of the wind turbine rotor.
- The first transient investigations concerned symmetrical airfoils from NACA 0012 to NACA 0021. When considering a wind turbine equipped with symmetrical NACA 0018 airfoils, the best aerodynamic performance was observed in the majority of tip speed ratio ranges.
- Although the NACA 0012 airfoil has the largest maximum lift coefficient of all symmetrical airfoils tested, it gives the worst results of the tangential blade load in the low tip speed ratio range. This is due to the worse airfoil characteristics in the detachment area compared to thicker airfoils.
- The analysis showed that symmetrical airfoils are much worse at low tip speed ratios. This is because of the worse characteristics of these airfoils in the stall regime. The introduction of one percent maximum camber greatly improves the aerodynamic performance of the rotor over the entire tip speed ratio range.
- The effect of the relative airfoil thickness on the characteristics of aerodynamic blade load components is larger at low tip speed ratios, whereas the maximum camber affects more of these characteristics at higher tip speed ratios.
- The use of cambered airfoils should improve the dynamic properties of the structure, e.g., reduce vibration. In the case of the NACA 4418 airfoil, the ratio of the maximum tangential blade load for the upwind part of the rotor to the downwind part is 88% lower compared to the NACA 0018 airfoil.
- The study examined the impact of tip speed ratio on the velocity distribution in the aerodynamic wake of a rotor equipped with NACA 0018 airfoils. Numerical analysis showed that as the tip speed ratio increases, and there is a linear decrease in the average velocity V
_{x}(velocity component parallel to the wind direction) of these profiles. In the case of the transverse velocity component V_{y}, its average for each tip speed ratio value is very close to zero. In the case of a rotor equipped with the symmetrical profile NACA 0018, it was observed that the share of the velocity component V_{y}in the aerodynamic shadow of the rotor is very low in the entire tested tip speed ratio range. - The increase in the relative thickness of symmetrical airfoils does not cause significant differences in the velocity distribution downstream behind the rotor in the entire investigated tip speed ratio range. The impact of maximum airfoil camber on the velocity distribution in aerodynamic shadow of the rotor is negligible. As in the case of symmetrical airfoils, the tip speed ratio has the biggest influence on the velocity distribution in the aerodynamic wake downstream behind the rotor.
- Good experimental data is really missing to further validate the low TSR results. More investigation on the influence by the different turbulence models is needed in future work, especially naturally unsteady models, such as LES and detached eddy simulation (DES).

## Author Contributions

## Funding

## Conflicts of Interest

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**Figure 8.**Aerodynamic airfoil characteristics: (

**a**) lift coefficient; (

**b**) drag coefficient. The comparison of CFD results with the experiment by Sheldahl and Klimas [64] and with the XFOIL predictions.

**Figure 9.**Aerodynamic airfoil characteristics of NACA 0012, NACA 0015, and NACA 0018: (

**a**) lift coefficient; (

**b**) drag coefficient. The comparison of CFD results with the experiment by Sheldahl and Klimas [64].

**Figure 10.**Aerodynamic blade load components: (

**a**) tangential component; (

**b**) normal component. Comparison of numerical results obtained with three different independent aerodynamic codes.

**Figure 11.**Aerodynamic blade load components for different maximum thickness of the NACA 4-digit airfoil: (

**a**) and (

**b**) present tangential and normal components, respectively at TSR of 2.0 whereas (

**c**) and (

**d**) at TSR of 5.0.

**Figure 12.**Static pressure (in Pascal) around the NACA 0012 airfoil at the rotor tip speed ratio of 2.

**Figure 13.**Static pressure (in Pascal) around the NACA 0018 airfoil at the rotor tip speed ratio of 2.

**Figure 16.**Aerodynamic blade load components, tangential component (on the left) and normal component (on the right), for different maximum camber of the NACA 4-digit airfoil and for two tip speed ratios, 2 and 5. Aerodynamic blade load components for different maximum camber of the NACA 4-digit airfoil: (

**a**) and (

**b**) present tangential and normal components, respectively at TSR of 2.0 whereas (

**c**) and (

**d**) at TSR of 5.0.

**Figure 17.**Rotor power coefficient as a function of maximum airfoil camber and tip speed ratio for t/c = 10%.

**Figure 18.**Velocity profiles downstream behind the rotor at the distance of 1.5 R form the rotor axis of rotation: (

**a**) velocity component parallel to the wind direction, V

_{x}; (

**b**) perpendicular to the wind direction. The results are given for the NACA 0018 airfoil and for five tip speed ratios. Velocities V

_{x}and V

_{y}are normalized by wind speed V

_{0}.

**Figure 21.**Velocity profiles downstream of the rotor at the distance of 1.5 R form the rotor axis; the maximum airfoil thickness effect: (

**a**) and (

**b**) velocity component parallel to the wind direction, V

_{x}, and velocity component perpendicular to the wind direction V

_{y}

_{,}respectively at TSR = 3 whereas (

**c**) and (

**d**) at TSR = 6.

**Figure 22.**Velocity profiles downstream of the rotor at the distance of 1.5 R form the rotor axis; the maximum airfoil camber effect: (

**a**) and (

**b**) velocity component parallel to the wind direction, V

_{x}, and velocity component perpendicular to the wind direction V

_{y}

_{,}respectively at TSR = 3 whereas (

**c**) and (

**d**) at TSR = 6.

Parameter | Value |
---|---|

Rotor radius, R | 8.84 [m] |

Blade length | 12.9 [m] |

Chord, c | 0.61 [m] |

Airfoil type | NACA 0018 |

Number of blades, B | 3 |

Rotor solidity, σ = Bc/R | 0.2 |

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**MDPI and ACS Style**

Rogowski, K.; Hansen, M.O.L.; Bangga, G. Performance Analysis of a H-Darrieus Wind Turbine for a Series of 4-Digit NACA Airfoils. *Energies* **2020**, *13*, 3196.
https://doi.org/10.3390/en13123196

**AMA Style**

Rogowski K, Hansen MOL, Bangga G. Performance Analysis of a H-Darrieus Wind Turbine for a Series of 4-Digit NACA Airfoils. *Energies*. 2020; 13(12):3196.
https://doi.org/10.3390/en13123196

**Chicago/Turabian Style**

Rogowski, Krzysztof, Martin Otto Laver Hansen, and Galih Bangga. 2020. "Performance Analysis of a H-Darrieus Wind Turbine for a Series of 4-Digit NACA Airfoils" *Energies* 13, no. 12: 3196.
https://doi.org/10.3390/en13123196